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In this paper, we investigate the beam domain statistical channel stateinformation (CSI) estimation for the two dimensional (2D) beam basedstatistical channel model (BSCM) in massive MIMO systems.The problem is toestimate the beam domain channel power matrices (BDCPMs) based on multiplereceive pilot signals. A receive model shows the relation between thestatistical property of the receive pilot signals and the BDCPMs is derivedfrom the 2D-BSCM. On the basis of the receive model,we formulate anoptimization problem with the Kullback-Leibler (KL) divergence. By solving theoptimization problem, a novel method to estimate the statistical CSI withoutinvolving instantaneous CSI is proposed. The proposed method has much lowercomplexity than the MMV focal underdetermined system solver (M-FOCUSS)algorithm. We further reduce the complexity of the proposed method by utilizingthe circulant structures of particular matrices in the algorithm. We alsoshowed the generality of the proposed method by introducing anotherapplication. Simulations results show that the proposed method works well andbring significant performance gain when used in channel estimation.

2D Beam Domain Statistical CSI Estimation for Massive MIMO Uplink